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Basic Math Concepts for Chemistry

*1.*Solve for density (d) in terms of molarity (ℳ), pressure (P), and temperature (T). (R) is a constant.*2.*Express y in terms of x: \(\frac{10}{4x}=\frac{3y}{8}\)*3.*Express a in terms of b: \(\frac{20a}{10b}=4+2b\)*4.*Find the solution set of \(x^3-3x^2=0\) from the replacement set {-3,0,3}.*5.*Find the integer solution set of \(2x^4+3x^3+2x-4=0\) from the replacement set {-2,-1,1,2}.*6.*Find the solution set of \(x^2-8=4\sqrt{x}\) from the replacement set {0,1,4,9}*7.*The United States National Weather Service reports pressure in both inches of Hg and millibars. Convert a pressure of 29.2 in. Hg into:

(a) torr

(b) atm

(c) kPa

(d) mbar*8.*A can of hair spray is used until it is empty except for the propellant, isobutane gas. The gas in the can is initially at 24 °C and 360 kPa, and the can has a volume of 350 mL. If the can is left in a car that reaches 50 °C on a hot day, what is the new pressure in the can?*9.*Methane, CH4, is being considered for use as an alternative automotive fuel to replace gasoline. One gallon of gasoline could be replaced by 655 g of CH4. What is the volume of this much methane at 25 °C and 745 torr?*10.*Methane, CH4, is being considered for use as an alternative automotive fuel to replace gasoline. One gallon of gasoline could be replaced by 655 g of CH4. What is the volume of this much methane at 25 °C and 745 torr?*11.*What is the density of common antifreeze in units of \(\frac{g}{mL}\)? A 4.00-qt sample of the antifreeze weighs 9.26 lb*12.*Normal body temperature has been commonly accepted as 37.0 °C (although it varies depending on time of day and method of measurement, as well as among individuals). What is this temperature on the kelvin scale and on the Fahrenheit scale?*13.*A rectangular plot in a garden has the dimensions 36.7 cm by 128.8 cm. What is the area of the garden plot in square meters? Express your answer in the proper number of significant figures.

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